2.1842   ODE No. 1842

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ x^2 y^{(3)}(x)+x y'(x)^2+(1-y(x)) y'(x)+x (y(x)-1) y''(x)=0 \] Mathematica : cpu = 0.15299 (sec), leaf count = 286

\[\left \{\left \{y(x)\to \frac {2 x \left (c_3 \left (J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-\frac {1}{4} i \sqrt {c_1} x \left (J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}-1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}+1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )\right )\right )+Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-\frac {1}{4} i \sqrt {c_1} x \left (Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}-1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}+1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )\right )\right )}{c_3 x J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )+x Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )}\right \}\right \}\] Maple : cpu = 1.368 (sec), leaf count = 190

\[ \left \{ \ln \left ( x \right ) +2\,\int ^{y \left ( x \right ) }\! \left ( 2\, \left ( {\it RootOf} \left ( -2\,\sqrt {4+{\it \_C1}}{{\sl Y}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_C2}+2\,{{\sl Y}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_C2}\,{\it \_h}-4\,{{\sl Y}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_C2}+2\,\sqrt {2}{{\sl Y}_{1/2\,\sqrt {4+{\it \_C1}}+1}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_C2}\,{\it \_Z}+2\,\sqrt {2}{{\sl J}_{1/2\,\sqrt {4+{\it \_C1}}+1}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_Z}-2\,{{\sl J}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )}\sqrt {4+{\it \_C1}}+2\,{{\sl J}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_h}-4\,{{\sl J}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )} \right ) \right ) ^{2}+{{\it \_h}}^{2}-{\it \_C1}-4\,{\it \_h} \right ) ^{-1}{d{\it \_h}}-{\it \_C3}=0 \right \} \]